doi:10.1038/nindia.2016.4 Published online 14 January 2016

Ecological science theory analyses stock market crashes


Borrowing the concept of ‘critical transitions’ from ecological sciences, researchers have analysed some historic financial market crashes of the past to reveal that there is no critical slowing down or ‘early warning signal’, as is believed, prior to such crashes1. However, there could be some wild fluctuations before major market meltdowns, they say.

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In ecology, critical transition is the phenomenon when complex natural systems sometimes suddenly tip over to a contrasting state. Some early warning signals (EWS) are believed to indicate that a system is approaching such a critical transition. In ecological and climatic transition studies, it has been shown that when there is a disturbance in the system, it takes longer to get back to its original state.

This observation, a group of mathematical ecologists and economists now believe, may not be true for financial market crashes.

Applying theories of complex systems and tipping points to financial markets, the researchers analysed daily closing data of three major U.S. markets (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) spanning the last century. They tested whether financial markets, using aggregate market indices, undergo critical transitions, close to tipping points and whether they provide any warning prior to financial meltdowns.

The study found that there is no critical slowing down before the crashes, although there are wild fluctuations. In other words, random disturbances and uncertainty can crash the markets even when they are not near a tipping point.

“Many papers suggest that financial meltdowns are also transitions near tipping points, but we show that they are actually driven by uncertainty (stochasticity) away from tipping points,” says Vishwesha Guttal, a mathematical ecologist at the Centre for Ecological Sciences at Indian Institute of Science (IISc) and co-author of the paper.

Srinivas Raghavendra, an economist from the National University Ireland Galway and a co-author, explains that common sense as well as the theory of critical transitions suggest that a bullish phase implies correlated behavior in the market. However, aggregate market data from DJI, S&P500, NASDAQ showed lack of autocorrelation prior to a crash.

“Lack of autocorrelation in the data surprised me. We even looked at the component level analysis, which showed a lack of autocorrelation,” he says.

Understanding the aggregate behavior of the market would lead to further insights as to what types of individual agent behavior might lead to such aggregate outcomes like crashes, he adds.

Anyone can apply these methods to analyse the market. Nikunj Goel, co-author and currently a Ph.D student at Yale University, has developed a basic web application that provides current trends in markets around the globe, including that of the Bombay Stock Exchange. “A user can select any stock index from a dropdown menu and obtain trends of systemic indicators for that day. The results can be downloaded,” Goel says. The programme code for the app has been made public so that it can be tweaked to suit individual user needs. 

According to Sitabhra Sinha at the Institute of Mathematical Sciences, Chennai, “There is evidence that markets exhibit log-periodic oscillations (periodic variations in fluctuations whose frequency changes as one gets closer to the crash event) suggestive of a critical transition. Guttal and his colleagues’ results do not necessarily contradict these results as they are arguing against transitions where the system moves from one stable state to another when the environment is altered.”

Probably, Sinha adds, it is more reasonable to think that markets move from one stochastic attractor to another – a phenomenon where the slowing down signature of critical transitions may be masked. 

Making sense of such a complex system as the financial market could be mind boggling. But Guttal sees a silver lining. “The fact that there has been increasing stochasticity prior to every crash, there is a funny element of determinism in it, right?" 


1. Guttal, V. et al. Lack of critical slowing down suggests that financial meltdowns are not critical transitions, yet rising variability could signal systemic risk. PLoS ONE (2016) doi: 10.1371/journal.pone.0144198